# Properties

 Label 380.2.i Level $380$ Weight $2$ Character orbit 380.i Rep. character $\chi_{380}(121,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $3$ Sturm bound $120$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$120$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(380, [\chi])$$.

Total New Old
Modular forms 132 16 116
Cusp forms 108 16 92
Eisenstein series 24 0 24

## Trace form

 $$16 q - 2 q^{3} - 4 q^{7} - 14 q^{9} + O(q^{10})$$ $$16 q - 2 q^{3} - 4 q^{7} - 14 q^{9} + 8 q^{11} + 6 q^{13} + 2 q^{17} + 10 q^{19} + 10 q^{23} - 8 q^{25} - 8 q^{27} - 2 q^{29} - 8 q^{31} + 16 q^{33} - 2 q^{35} - 56 q^{37} - 28 q^{39} - 16 q^{41} + 12 q^{43} - 8 q^{45} + 16 q^{47} + 32 q^{49} - 16 q^{51} + 24 q^{53} + 36 q^{57} + 18 q^{59} + 12 q^{61} + 6 q^{63} - 24 q^{65} + 10 q^{67} + 52 q^{69} + 8 q^{71} + 2 q^{73} + 4 q^{75} + 20 q^{77} - 18 q^{79} - 36 q^{81} - 20 q^{83} - 12 q^{87} - 14 q^{89} - 20 q^{91} - 4 q^{93} - 4 q^{95} - 24 q^{97} + 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(380, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.i.a $2$ $3.034$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$1$$ $$-8$$ $$q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-4q^{7}+\cdots$$
380.2.i.b $6$ $3.034$ 6.0.1783323.2 None $$0$$ $$1$$ $$3$$ $$4$$ $$q+(\beta _{3}-\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots$$
380.2.i.c $8$ $3.034$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$-1$$ $$-4$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(380, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(380, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$